One of his best stories to include fly fishing, I think, is "Big Two-Hearted River". It's a story about a man going back to fish the rivers of his youth, alone, in order to recover & recoup from the horrors of war he has recently witnessed. From a literary point of view, the story was innovative, in that the plot is implied, rather than fully stated. No matter, if you love to fly fish you will enjoy this short story. It has all the elements we fly fishers love: beautiful wilderness, trout, & the challenges of catching them.
Hemingway was also a skilled salt water angler too, especially for big game fish like tuna & marlin. It's believed he could have set many records for those fish.
If you're looking for some good reading, & want to include some fishing stories, you might want to re-visit, or for some of you discover, the works of Ernest Hemingway. Here is a short video about some of his fishing accomplishments: